Logic

Chess Abstract: Level 2 Challenges

On the left, we have a $$3 \times 3$$ board with 4 knights, where the white knights and black knights are separated vertically.

Using standard chess moves, is it possible to integrate the knights into the position on the right?

What is the minimum number of moves "white" could make to win this game?

Note: Assume that the black doesn't resign, but that he plays into white's gambit so as to lose the game as quickly as possible.

A new piece in chess has been introduced. Instead of being like the knight, which moves two spaces horizontally and one space vertically or two spaces vertically and one space horizontally, the new piece moves three spaces horizontally and one space vertically or three spaces vertically and one space horizontally.

The piece is now on the square labelled "A". What is the least number of moves it needs to have to get to the square labelled "B"?

Two opposite corner squares are detached from the chessboard.

Is it possible to make a path for a knight such that it visited all of the square once and only once? If yes, how many ways are there?

What is the maximum number of pawns that can be placed on an $$8\times 8$$ chessboard such that each row, each column, and each long diagonal contains at most 4 pawns?

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